text: Faxén's laws are direct relations that express the multipole moments in terms of the ambient flow and its derivatives.  First developed by Hilding Faxén to calculate the force, , and torque,  on a sphere, they take the following form:
  where  is the dynamic viscosity,  is the particle radius,  is the ambient flow,  is the speed of the particle,  is the angular velocity of the background flow, and  is the angular velocity of the particle.
  Faxén's laws can be generalized to describe the moments of other shapes, such as ellipsoids, spheroids, and spherical drops.